taneja.niks wrote:This is one form the princeton material

Are V and W integers?
1. root(v+w) is an integer
2.v/w is an integer

please help with the answer and explanation

root(4.5+4.5) = root(9) is integer... But 4.5 is not
So NO
root(6+3) = root(9) = integer..so YES

7.5/2.5 = 3 = integer.. so V,W are not integers..so NO
6/3 = 2 = integer.. so V,W are integers so YES

combining both:
4.5/4.5 is integer and root(4.5+4.5) is integer..
So answer is NO

6/3 is an integer and root(6+3) is integer
Here answer is YES.

Hence Picke E

Hope this helps!!

Are V and W integers?

1. root(v+w) is an integer.

eg. 1. root(2+7) = root(9) = 3
2. root(3/7 + 25/7) = root(4) = 2

Insufficient.

2. v/w is an integer. (say n)

Thus v = n.w

If n = 1 for example, v and w could both be integers or both equal fractions as well.

Insufficient

Both 1 and 2:

root(v + w) = root ( nw + w) = root [w(n+1)]

This means that w*(n+1) is a perfect square.

n+1 is going to be an integer.
But again w may or may not be an integer.

eg. n = 2, w = 4/3 => w*(n+1) = 4/3 * 3 = 4
n = 2, w =3 => w*(n+1) = 3*3 = 9

Thus, it is still insufficient.

Pick E.